Estimation in a Competing Risks Proportional Hazards Model Under Length-biased Sampling With Censoring

International audienceWhat population does the sample represent? The answer to this question is of crucial importance when estimating a survivor function in duration studies. As is well-known, in a stationary population, survival data obtained from a cross-sectional sample taken from the population at time $t_0$ represents not the target density $f(t)$ but its length-biased version proportional to $tf(t)$, for $t>0$. The problem of estimating survivor function from such length-biased samples becomes more complex, and interesting, in presence of competing risks and censoring. This paper lays out a sampling scheme related to a mixed Poisson process and develops nonparametric estimators of the survivor function of the target population assuming that the two independent competing risks have proportional hazards. Two cases are considered: with and without independent consoring before length biased sampling. In each case, the weak convergence of the process generated by the proposed estimator is proved. A well-known study of the duration in power for political leaders is used to illustrate our results. Finally, a simulation study is carried out in order to assess the finite sample behaviour of our estimators

A copula model for dependent competing risks

Many popular estimators for duration models require independent competing risks or independent censoring. In contrast, copula based estimators are also consistent in presence of dependent competing risks. In this paper we suggest a computationally convenient extension of the Copula Graphic Estimator (Zheng and Klein, 1995) to a model with more than two dependent competing risks. We analyse the applicability of this estimator by means of simulations and real world unemployment duration data from Germany. We obtain evidence that our estimator yields nice results if the dependence structure is known and that it is a powerful tool for the assessment of the relevance of (in-)dependence assumptions in applied duration research.Archimedean copula, dependent censoring, unemployment duration

Nonparametric Analysis of Hedge Funds Lifetimes

Most of hedge funds databases are now keeping history of dead funds in order to control biases in empirical analysis. It is then possible to use these data for the analysis of hedge funds lifetimes and survivorship. This paper proposes two nonparametric specifications of duration models. First, the single risk model is an alternative to parametric duration models used in the literature. Second, the competing risks model consider the two reasons why hedge funds stop reporting. We apply the two models to hedge funds data and compare our results to the literature. In particular, we show that a cohort effect must be considered. Moreover, the reason of the exit is a crucial information for the analysis of funds' survival as for a large part of disappearing funds, exit cannot be explained by low performance or low level of assets.

A copula model for dependent competing risks

"Many popular estimators for duration models require independent competing risks or independent censoring. In contrast, copula based estimators are also consistent in presence of dependent competing risks. In this paper we suggest a computationally convenient extension of the Copula Graphic Estimator (Zheng and Klein, 1995) to a model with more than two dependent competing risks. We analyse the applicability of this estimator by means of simulations and real world unemployment duration data from Germany. We obtain evidence that our estimator yields nice results if the dependence structure is known and that it is a powerful tool for the assessment of the relevance of (in-)dependence assumptions in applied duration research." (Author's abstract, IAB-Doku) ((en)) Additional Information Appendix for the FDZ-Methodenreport No. 02/2009Risikoabschätzung - Modell, Wirkungsforschung - Methode, Methodologie, Arbeitsmarktpolitik - Erfolgskontrolle, ältere Arbeitnehmer, Leistungsanspruch - Dauer, Arbeitslosigkeitsdauer, IAB-Beschäftigtenstichprobe

On the Statistical Modeling and Analysis of Repairable Systems

We review basic modeling approaches for failure and maintenance data from repairable systems. In particular we consider imperfect repair models, defined in terms of virtual age processes, and the trend-renewal process which extends the nonhomogeneous Poisson process and the renewal process. In the case where several systems of the same kind are observed, we show how observed covariates and unobserved heterogeneity can be included in the models. We also consider various approaches to trend testing. Modern reliability data bases usually contain information on the type of failure, the type of maintenance and so forth in addition to the failure times themselves. Basing our work on recent literature we present a framework where the observed events are modeled as marked point processes, with marks labeling the types of events. Throughout the paper the emphasis is more on modeling than on statistical inference.Comment: Published at http://dx.doi.org/10.1214/088342306000000448 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bounds analysis of competing risks : a nonparametric evaluation of the effect of unemployment benefits on migration in Germany

"In this paper we derive nonparametric bounds for the cumulative incidence curve within a competing risks model with partly identified interval data. As an advantage over earlier attempts our approach also gives valid results in case of dependent competing risks. We apply our framework to empirically evaluate the effect of unemployment benefits on observed migration of unemployed workers in Germany. Our findings weakly indicate that reducing the entitlement length for unemployment benefits increases migration among high-skilled individuals." (Author's abstract, IAB-Doku) ((en))Arbeitslosenunterstützung, Leistungsanspruch - Dauer, Binnenwanderung, regionale Mobilität, Wanderungsmotivation, Mobilitätsbereitschaft, Arbeitslose, Hochqualifizierte, IAB-Beschäftigtenstichprobe

Bounds Analysis of Competing Risks: A Nonparametric Evaluation of the Effect of Unemployment Benefits on Imigration in Germany

In this paper we derive nonparametric bounds for the cumulative incidence curve within a competing risks model with partly identified interval data. As an advantage over earlier attempts our approach also gives valid results in case of dependent competing risks. We apply our framework to empirically evaluate the effect of unemployment benefits on observed migration of unemployed workers in Germany. Our findings weakly indicate that reducing the entitlement length for unemployment benefits increases migration among high-skilled individuals. --cumulative incidence curve,partially missing data,bounds analysis,difference-in-differences

Reform of unemployment compensation in Germany: a nonparametric bounds analysis using register data

Economic theory suggests that an extension of the maximum length of entitlement for unemployment benefits increases the duration of unemployment. Empirical results for the reform of the unemployment compensation system in Germany during the 1980s are less clear. The analysis in this paper is motivated by the controversial empirical findings and by recent developments in econometrics for partial identification. We use extensive administrative data with the drawback that registered unemployment is not directly observed. For this reason we bound the reform effect on unemployment duration over different definitions of unemployment. By exploiting the richness of the data we use a nonparametric approach without imposing critical parametric model assumptions. We identify a systematic increase in unemployment duration in response to the reform in samples that amount to less than 15% of the unemployment spells for the treatment group.unemployment duration, definition of unemployment, nonparametric